But, using this vector directly will move/warp your character directly to the mouse cursor, so you might want to scale it down a bit. Ofc, if you where using vectors, this would be easier (e.g. you could multiply the normalized direction by a speed instead of using a scaleFactor).

To move to either the side, you would need to move to a direction -90° or 90° from the forward direction.

Edit:
The distance between the character and mouse cursor influences the above formula, thus the character moves faster the further the mouse is away.

This can be changed to be a constant speed by either calculating a constant direction from the characters rotation (using trigonometric functions) or by normalizing the direction vector. In both cases, the result is multiplied by the characters speed and added to her position.